# Free SAT Math Diagnostic Tests

Take the Varsity Learning Tools free diagnostic test for SAT Math to determine which academic concepts you understand and which ones require your ongoing attention. Each SAT Math problem is tagged down to the core, underlying concept that is being tested. The SAT Math diagnostic test results highlight how you performed on each area of the test. You can then utilize the results to create a personalized study plan that is based on your particular area of need.

### All SAT Math Resources

Our free SAT Math Practice Tests are each a selection of 10 to 12 questions, which will give you a cross-section of topics from the Math section of the official SAT. You might think of them as little quizzes, which you can use to hone your skills. Whether you need SAT Math tutoring in New York, SAT Math tutoring in Chicago, or SAT Math tutoring in Los Angeles, working one-on-one with an expert may be just the boost your studies need.

SAT Mathematics Section

What kind of math concepts does the SAT Math section test?

The SAT Math section tests a student’s ability to perform basic arithmetic, and solve problems based on concepts drawn from algebra (1 & 2), geometry, probability, and statistics. Students are also required to analyze charts and graphs and answer questions about the data that those charts and graphs present. Varsity Tutors also offers resources like a free SAT prep book to help with your self-paced study, or you may want to consider an SAT Math tutor.

The content that the SAT Math section tests can be broken down into four sections: Numbers and Operations; Algebra and Functions; Geometry and Measurement; and Data Analysis, Statistics, and Probability. These sections test the following content:

Number and Operations

Arithmetic word problems (including percent, ratio, and proportion)

Properties of integers (even, odd, prime numbers, divisibility, etc.)

Rational numbers

Sets (union, intersection, elements)

Counting techniques

Sequences and series (including exponential growth)

Elementary number theory

Algebra and Functions

Arithmetic word problems (including percent, ratio, and proportion)

Properties of integers (even, odd, prime numbers, divisibility, etc.)

Rational numbers

Sets (union, intersection, elements)

Counting techniques

Sequences and series (including exponential growth)

Elementary number theory

Geometry and Measurement

Area and perimeter of a polygon

Area and circumference of a circle

Volume of a box, cube, and cylinder

Pythagorean Theorem and special properties of isosceles, equilateral, and right triangles

Properties of parallel and perpendicular lines

Coordinate geometry

Geometric visualization

Slope

Similarity

Transformations

Data Analysis, Statistics, and Probability

Data interpretation (tables and graphs)

Descriptive statistics (mean, median, and mode)

Probability

What types of questions appear on the SAT Math section?

Two types of questions appear on the SAT Math section: multiple-choice questions and grid-in questions.

Multiple-choice questions consist of a problem followed by five potentially correct answers; in order to answer a question, you select the answer you believe to be correct and bubble in its corresponding letter on your answer sheet.

Grid-in questions consist of a problem followed by four consecutive boxes. Each box corresponds to a column of bubbles directly underneath it, which each contain the symbol for a fraction line, a decimal, and the numbers 0-9. (The first box’s column omits the zero so that students don’t bubble in zeroes before their decimals.) After determining the correct answer to the problem, you both write out your response in the boxes and bubble in each number’s corresponding bubble underneath it.

Remember the following points when completing grid-in questions:

Answers may be either right-justified or left-justified (i.e. you may have a blank box on either the right or left side of a three-digit answer). However, it is recommended that you pick one of these and stick with it during the test, so that you don’t get confused and accidentally bubble in an incorrect answer.

Bubble in only one circle per column.

Don’t bubble in any circle for columns that you do not need.

Your answer is based on the bubbled-in numbers, not the numbers you write in the boxes. So, make sure that you bubble in your answer correctly!

Some questions may have multiple correct answers; if so, bubble in only one.

No grid-in problem will have a negative answer.

Mixed numbers like 7 ⅓ need to be submitted as decimal answers (i.e. 7.333) or fractions (i.e. 22/3). If you bubble in “7 1 / 2,” it will be assumed that you mean 71/2, not 7½.

Decimal answers with repeating digits are too big for the grid should NOT be rounded down so that empty spaces appear on the grid. For instance, if you get ⅓ as an answer and choose to grid it as a decimal, you need to write “. 3 3 3,” not “. 3 3,” which would be marked wrong because it’s not as accurate as it can be. For decimal answers with repeating digits that need to be rounded, i.e. ⅔, either “. 6 6 6” or “. 6 6 7” is an acceptable answer.

How many problems are on the SAT Math section, and how much time will I have to complete them?

The SAT Math section consists of 54 questions in total. 44 of these questions are multiple-choice and 10 are grid-in. These questions appear on three sections of the test, two of which are 25 minutes long and one of which is 20 minutes long. These sections are interspersed amongst Critical Reading and Writing sections, so you don’t do them consecutively. Given that you have 54 questions to complete in 70 minutes, you have about one minute and fifteen seconds per question.

Math Section #1: 20 multiple-choice questions / 25 minutes

Math Section #2: 8 multiple-choice questions followed by 10 grid-in questions / 25 minutes

Math Section #3: 16 multiple-choice questions / 20 minutes

Total: 54 questions (44 multiple-choice and 10 grid-in) / 70 minutes

Can I use a calculator on the SAT Math section?

Yes! Students should bring their own calculator—a scientific calculator is recommended, but certain graphing calculators are permitted. While calculators are extremely useful on some problems, they can slow you down on others where it’s better to simplify equations or estimate.

Which kinds of calculators are permitted on the SAT Math section?

Calculators are only permitted on the Math section of the SAT. Four-function calculators are permitted, but not recommended; scientific calculators (whether programmable or non-programmable) are permitted; and the graphing calculators listed below are permitted.

Casio: FX-6000 series, FX-6200 series, FX-6300 series, FX-6500 series, FX-7000 series, FX-7300 series, FX-7400 series, FX-7500 series, FX-7700 series, FX-7800 series, FX-8000 series, FX-8500 series, FX-8700 series, FX-8800 series, FX-9700 series, FX-9750 series, FX-9860 series, CFX-9800 series, CFX-9850 series, CFX-9950 series, CFX-9970 series, FX 1.0 series, Algebra FX 2.0 series, FX-CG-10 (PRIZM), FX-CG-20

Hewlett-Packard: HP-9G, HP-28 series, HP-38G, HP-39 series, HP-40 series, HP-48 series, HP-49 series, HP-50 series

Sharp: EL-5200, EL-9200, EL-9300, EL-9600*, EL-9900

*You are not permitted to use the stylus with the Sharp EL-9600 calculator on the SAT.

Texas Instruments: TI-73, TI-80, TI-81, TI-82, TI-83/TI-83 Plus, TI-83 Plus Silver, TI-84 Plus, TI-84 Plus Silver, TI-85, TI-86, TI-89, TI-89 Titanium, TI-Nspire/TI-Nspire CX, TI-Nspire CAS/TI-Nspire CX CAS, TI-Nspire CM-C, TI-Nspire CAS CX-C

Other: Datexx DS-883, Micronta, Smart2

You are NOT permitted to use any of the following devices as a calculator on the SAT:

Laptop or portable/handheld computer

Calculator that has a QWERTY (keyboard-like) keypad, uses an electrical outlet, makes noise or has a paper tape

Electronic writing pad or pen-input/stylus-driven device

Pocket organizer

Calculator function on a mobile phone

What if I forget an important formula on the SAT Math section?

On the SAT, all of the major formulas covered on the test—including the areas and volumes of shapes like circles, triangles, and quadrilaterals, and the surface areas and volumes of three-dimensional shapes—are included on the test for your reference. While this may seem like an excuse not to learn them, knowing the formulas yourself and only referencing the included reference material to double-check what you already know will save you a lot of time on the SAT Math section.

The following images and formulas are provided on the SAT Math booklet and are available for reference during the exam:

An image of a circle with the radius identified as “r”

A = πr2

C = 2πr

An image of a rectangle with the length identified as “l” and the width identified as “w”

A = lw

An image of a triangle with the height identified as “h” and the base identified as “b”

A = ½bh

An image of a three-dimensional rectangle with length identified as “l,” width identified as “w,” and height identified as “h”

V = lwh

An image of a cylinder with its radius identified as “r” and its height identified as “h”

V = πr2h

An image of a right triangle with its legs labeled “a” and “b” and its hypotenuse labeled “c”

c2 = a2 + b2

Special Right Triangles

An image of a 30-60-90 triangle with its angles appropriately labeled, the side opposite the 30º labeled “x,” the side opposite the 60º angle labeled “x√3,” and the side opposite the 90º angle (the hypotenuse) labeled “2x.”

An image of a 45-45-90 triangle with its angles appropriately labeled, each leg labeled “s,” and the hypotenuse labeled “s√2”

The following sentences are also included:

“The number of degrees of arc in a circle is 360.”

“The sum of the measures in degrees of the angles of a triangle is 180.”

Should I guess on the SAT Math section?

It depends. On multiple choice questions, there is a deduction of ¼ point for choosing the wrong answer, so you don’t want to guess randomly; however, if you can eliminate a few wrong answers and guess between the remaining ones, you will have a better chance of guessing correctly on multiple-choice questions. So, narrowing down the number of potentially correct answers is a good strategy on multiple-choice questions, but won’t work with the grid-ins, where you are required to write out the answer.

Where are the easy questions on the SAT Math section?

The SAT is relatively straightforward here: questions in each section start off easy and become more difficult as you go on. Since all questions have the same score (1 point for a correct answer), it’s a good strategy to make sure all the easy and medium questions in the beginning of the section are answered correctly before working on the difficult problems near the end.

How should I study for the SAT Math section?

Varsity Tutors offers free SAT Math Practice Tests for you to use in preparing for the SAT's Math section. Our free SAT Math Practice Tests are written by teachers, professors, content specialists, and tutors. Explanations are given for each question, so if you miss a question, you can find out where you went wrong. In addition to the SAT Math Practice Tests and SAT Math tutoring, you may also want to consider using some of our SAT Math flash cards. Varsity Tutors also offers free SAT Math Questions of the Day, free SAT Math Full-Length Tests, and other free SAT Math resources.